Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data

Authors:
Michael Kohler;Adam Krzyżak;Harro Walk
Affiliations:
Department of Mathematics, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany;Department of Computer Science and Software Engineering, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, Canada H3G 1M8;Department of Mathematics, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Venue:
Journal of Multivariate Analysis
Year:
2006

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Abstract

Estimation of regression functions from independent and identically distributed data is considered. The L"2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on the regression function and moment conditions on Y also boundedness assumptions on X are made. In this article we consider partitioning and nearest neighbor estimates and show that by replacing the boundedness assumption on X by a proper moment condition the same rate of convergence can be shown as for bounded data.